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<h1>v_teager
</h1>

<h2><a name="_name"></a>PURPOSE <a href="#_top"><img alt="^" border="0" src="../up.png"></a></h2>
<div class="box"><strong>V_TEAGER calculate v_teager energy waveform Y=(X,D,M)</strong></div>

<h2><a name="_synopsis"></a>SYNOPSIS <a href="#_top"><img alt="^" border="0" src="../up.png"></a></h2>
<div class="box"><strong>function y=v_teager(x,d,m) </strong></div>

<h2><a name="_description"></a>DESCRIPTION <a href="#_top"><img alt="^" border="0" src="../up.png"></a></h2>
<div class="fragment"><pre class="comment">V_TEAGER calculate v_teager energy waveform Y=(X,D,M)

  Inputs:  x         speech signal
           d         dimension to apply filter along [default 1st non-singleton]
           m         Normally Y has the same length as X and the first
                     and last output samples are extrapolated. Setting m='x'
                     supresses this extrapolation and Y will be two
                     samples shorter than X

 Outputs:  Y         output signal: y(n)=abs(x(n))^2 - x(n+1)*conj(x(n-1))

 Calculates the Teager energy waveform [1]. The following waveforms give
 a constant output (independent of n) where A, B, C are real constants:
  (a) x(n) = A*sin(B*n+C)    --&gt;   y(n) = (A*sin(B))^2
  (b) x(n) = A*n + B         --&gt;   y(n) = A^2
  (c) x(n) = A*exp(j(B*n+C)) --&gt;   y(n) = A^2*(1-exp(2jB))
  (d) x(n) = A*exp(B*n+C)    --&gt;   y(n) = 0

 Reference:
  [1]    J. Kaiser. On a simple algorithm to calculate the &quot;energy&quot; of a signal.
       In Proc IEEE Intl Conf Acoustics, Speech and Signal Processing,
       pages 381-384, vol.1, Apr. 1990. doi: 10.1109/ICASSP.1990.115702.</pre></div>

<!-- crossreference -->
<h2><a name="_cross"></a>CROSS-REFERENCE INFORMATION <a href="#_top"><img alt="^" border="0" src="../up.png"></a></h2>
This function calls:
<ul style="list-style-image:url(../matlabicon.gif)">
</ul>
This function is called by:
<ul style="list-style-image:url(../matlabicon.gif)">
</ul>
<!-- crossreference -->


<h2><a name="_source"></a>SOURCE CODE <a href="#_top"><img alt="^" border="0" src="../up.png"></a></h2>
<div class="fragment"><pre>0001 <a name="_sub0" href="#_subfunctions" class="code">function y=v_teager(x,d,m)</a>
0002 <span class="comment">%V_TEAGER calculate v_teager energy waveform Y=(X,D,M)</span>
0003 <span class="comment">%</span>
0004 <span class="comment">%  Inputs:  x         speech signal</span>
0005 <span class="comment">%           d         dimension to apply filter along [default 1st non-singleton]</span>
0006 <span class="comment">%           m         Normally Y has the same length as X and the first</span>
0007 <span class="comment">%                     and last output samples are extrapolated. Setting m='x'</span>
0008 <span class="comment">%                     supresses this extrapolation and Y will be two</span>
0009 <span class="comment">%                     samples shorter than X</span>
0010 <span class="comment">%</span>
0011 <span class="comment">% Outputs:  Y         output signal: y(n)=abs(x(n))^2 - x(n+1)*conj(x(n-1))</span>
0012 <span class="comment">%</span>
0013 <span class="comment">% Calculates the Teager energy waveform [1]. The following waveforms give</span>
0014 <span class="comment">% a constant output (independent of n) where A, B, C are real constants:</span>
0015 <span class="comment">%  (a) x(n) = A*sin(B*n+C)    --&gt;   y(n) = (A*sin(B))^2</span>
0016 <span class="comment">%  (b) x(n) = A*n + B         --&gt;   y(n) = A^2</span>
0017 <span class="comment">%  (c) x(n) = A*exp(j(B*n+C)) --&gt;   y(n) = A^2*(1-exp(2jB))</span>
0018 <span class="comment">%  (d) x(n) = A*exp(B*n+C)    --&gt;   y(n) = 0</span>
0019 <span class="comment">%</span>
0020 <span class="comment">% Reference:</span>
0021 <span class="comment">%  [1]    J. Kaiser. On a simple algorithm to calculate the &quot;energy&quot; of a signal.</span>
0022 <span class="comment">%       In Proc IEEE Intl Conf Acoustics, Speech and Signal Processing,</span>
0023 <span class="comment">%       pages 381-384, vol.1, Apr. 1990. doi: 10.1109/ICASSP.1990.115702.</span>
0024 
0025 <span class="comment">%      Copyright (C) Mike Brookes 1997</span>
0026 <span class="comment">%      Version: $Id: v_teager.m 10865 2018-09-21 17:22:45Z dmb $</span>
0027 <span class="comment">%</span>
0028 <span class="comment">%   VOICEBOX is a MATLAB toolbox for speech processing.</span>
0029 <span class="comment">%   Home page: http://www.ee.ic.ac.uk/hp/staff/dmb/voicebox/voicebox.html</span>
0030 <span class="comment">%</span>
0031 <span class="comment">%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%</span>
0032 <span class="comment">%   This program is free software; you can redistribute it and/or modify</span>
0033 <span class="comment">%   it under the terms of the GNU General Public License as published by</span>
0034 <span class="comment">%   the Free Software Foundation; either version 2 of the License, or</span>
0035 <span class="comment">%   (at your option) any later version.</span>
0036 <span class="comment">%</span>
0037 <span class="comment">%   This program is distributed in the hope that it will be useful,</span>
0038 <span class="comment">%   but WITHOUT ANY WARRANTY; without even the implied warranty of</span>
0039 <span class="comment">%   MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the</span>
0040 <span class="comment">%   GNU General Public License for more details.</span>
0041 <span class="comment">%</span>
0042 <span class="comment">%   You can obtain a copy of the GNU General Public License from</span>
0043 <span class="comment">%   http://www.gnu.org/copyleft/gpl.html or by writing to</span>
0044 <span class="comment">%   Free Software Foundation, Inc.,675 Mass Ave, Cambridge, MA 02139, USA.</span>
0045 <span class="comment">%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%</span>
0046 e=size(x);
0047 p=prod(e);
0048 <span class="keyword">if</span> nargin&lt;2             <span class="comment">% if no dimension given, find the first non-singleton</span>
0049     d=find(e&gt;1,1);
0050     <span class="keyword">if</span> ~numel(d)
0051         d=1;
0052     <span class="keyword">end</span>
0053 <span class="keyword">end</span>
0054 k=e(d);                 <span class="comment">% size of active dimension</span>
0055 q=p/k;                  <span class="comment">% size of remainder</span>
0056 <span class="keyword">if</span> d==1
0057     z=reshape(x,k,q);
0058 <span class="keyword">else</span>
0059     z=shiftdim(x,d-1);
0060     r=size(z);
0061     z=reshape(z,k,q);
0062 <span class="keyword">end</span>
0063 <span class="keyword">if</span> nargin&gt;2 &amp;&amp; any(m==<span class="string">'x'</span>)
0064     y=z(2:k-1,:).*conj(z(2:k-1,:))-z(3:k,:).*conj(z(1:k-2,:));
0065     k=k-2;              <span class="comment">% we have lost two elements</span>
0066 <span class="keyword">elseif</span> k&gt;=4
0067     y=zeros(k,q);
0068     y(2:k-1,:)=z(2:k-1,:).*conj(z(2:k-1,:))-z(3:k,:).*conj(z(1:k-2,:));
0069     y(1,:)=2*y(2,:)-y(3,:);             <span class="comment">% linearly interpolate the end points</span>
0070     y(k,:)=2*y(k-1,:)-y(k-2,:);
0071 <span class="keyword">elseif</span> k==3
0072     y=repmat(x(2,:).*conj(x(2,:))-x(3,:).*conj(x(1,:)),3,1);
0073 <span class="keyword">else</span>
0074     y=zeros(k,q);
0075 <span class="keyword">end</span>
0076 <span class="keyword">if</span> d==1
0077     e(d)=k;
0078     y=reshape(y,e);
0079 <span class="keyword">else</span>
0080     r(1)=k;
0081     y=shiftdim(reshape(y,r),length(e)+1-d);
0082 <span class="keyword">end</span></pre></div>
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